Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Treatment Effect Estimation for Optimal Decision-Making

Dennis Frauen, Valentyn Melnychuk, Jonas Schweisthal, Mihaela van der Schaar, Stefan Feuerriegel

TL;DR

This work addresses the gap between CATE estimation and optimal decision-making by showing that thresholding two-stage CATE estimators can be suboptimal when targeting policy value. It introduces policy-targeted CATE (PT-CATE) with a gamma-parameterized objective and an adaptive indicator to jointly optimize CATE accuracy and decision performance, implemented via a three-stage neural algorithm. The approach comes with theoretical guarantees (suboptimality results and nuisance-error bounds) and empirical evidence on synthetic and real data demonstrating improved decision quality with controlled CATE trade-offs. The method preserves interpretability through a CATE-like representation while delivering practical gains for data-driven decision-making in fields like medicine and marketing.

Abstract

Decision-making across various fields, such as medicine, heavily relies on conditional average treatment effects (CATEs). Practitioners commonly make decisions by checking whether the estimated CATE is positive, even though the decision-making performance of modern CATE estimators is poorly understood from a theoretical perspective. In this paper, we study optimal decision-making based on two-stage CATE estimators (e.g., DR-learner), which are considered state-of-the-art and widely used in practice. We prove that, while such estimators may be optimal for estimating CATE, they can be suboptimal when used for decision-making. Intuitively, this occurs because such estimators prioritize CATE accuracy in regions far away from the decision boundary, which is ultimately irrelevant to decision-making. As a remedy, we propose a novel two-stage learning objective that retargets the CATE to balance CATE estimation error and decision performance. We then propose a neural method that optimizes an adaptively-smoothed approximation of our learning objective. Finally, we confirm the effectiveness of our method both empirically and theoretically. In sum, our work is the first to show how two-stage CATE estimators can be adapted for optimal decision-making.

Treatment Effect Estimation for Optimal Decision-Making

TL;DR

This work addresses the gap between CATE estimation and optimal decision-making by showing that thresholding two-stage CATE estimators can be suboptimal when targeting policy value. It introduces policy-targeted CATE (PT-CATE) with a gamma-parameterized objective and an adaptive indicator to jointly optimize CATE accuracy and decision performance, implemented via a three-stage neural algorithm. The approach comes with theoretical guarantees (suboptimality results and nuisance-error bounds) and empirical evidence on synthetic and real data demonstrating improved decision quality with controlled CATE trade-offs. The method preserves interpretability through a CATE-like representation while delivering practical gains for data-driven decision-making in fields like medicine and marketing.

Abstract

Decision-making across various fields, such as medicine, heavily relies on conditional average treatment effects (CATEs). Practitioners commonly make decisions by checking whether the estimated CATE is positive, even though the decision-making performance of modern CATE estimators is poorly understood from a theoretical perspective. In this paper, we study optimal decision-making based on two-stage CATE estimators (e.g., DR-learner), which are considered state-of-the-art and widely used in practice. We prove that, while such estimators may be optimal for estimating CATE, they can be suboptimal when used for decision-making. Intuitively, this occurs because such estimators prioritize CATE accuracy in regions far away from the decision boundary, which is ultimately irrelevant to decision-making. As a remedy, we propose a novel two-stage learning objective that retargets the CATE to balance CATE estimation error and decision performance. We then propose a neural method that optimizes an adaptively-smoothed approximation of our learning objective. Finally, we confirm the effectiveness of our method both empirically and theoretically. In sum, our work is the first to show how two-stage CATE estimators can be adapted for optimal decision-making.
Paper Structure (28 sections, 4 theorems, 56 equations, 12 figures, 1 table, 1 algorithm)

This paper contains 28 sections, 4 theorems, 56 equations, 12 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related work
  3. Problem setup
  4. Setting
  5. Mathematical preliminaries
  6. Research questions
  7. Retargeting CATE for decision-making
  8. Suboptimality of CATE for decision-making
  9. A novel learning objective for retargeting CATE
  10. Estimated nuisance functions
  11. Learning algorithm
  12. Experiments
  13. Discussion
  14. Extended related work
  15. Deep learning for CATE estimation
  16. ...and 13 more sections

Key Result

Theorem 4.1

Let $\mathcal{G}$ be a class of neural networks with fixed architecture. Then, there exists a CATE $\tau^\ast \notin \mathcal{G}$, so that, for any optimal CATE approximation $g^\ast_{\tau^\ast} \in \arg\min_{g \in \mathcal{G}} \mathbb{E}[(\tau^\ast(X) - g(X))^2]$, it holds that $V_{\tau^\ast}(\pi_{

Figures (12)

  • Figure 1: Illustrative example showing the suboptimality of CATE estimation for decision-making. The dotted lines show regularized two-stage CATE estimators. The blue line corresponds to standard two-stage CATE estimation, while the green and violet lines are generated by our method. The parameter $\gamma$ quantifies the trade-off between CATE estimation error and decision-making performance. Details are in Sec. \ref{['sec:experiments']}.
  • Figure 2: Experimental results for our proposed method with $\mathcal{G}$ being the class of linear models.Left: CATE estimator (blue) is the best linear approximation of the (nonlinear) ground-truth CATE (red). Center: the trained $\alpha(X)$ detects the region in which the estimated CATE has the wrong sign. Right: retargeted CATE estimators using our proposed loss with trained $\alpha(X)$ and different $\gamma$ values.
  • Figure 3: Overview of our second-stage architecture and our learning algorithm.
  • Figure 4: Experimental results for setting A. Shown: PEHE and policy loss over $\gamma$ (lower $=$ better). Shown: mean and standard errors over $5$ runs.
  • Figure 5: Experimental results for setting B. Shown: PEHE and policy loss over $\gamma$ (lower $=$ better). Shown: mean and standard errors over $5$ runs.
  • ...and 7 more figures

Theorems & Definitions (11)

  • Theorem 4.1: Suboptimality of CATE-based decision-making
  • proof
  • Definition 4.2
  • Theorem 4.3: Consistency
  • proof
  • Theorem 4.4: Error rates
  • proof
  • proof
  • proof
  • Theorem B.1
  • ...and 1 more